/
tr_condensate1.py
300 lines (208 loc) · 8.61 KB
/
tr_condensate1.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
# -*- coding: utf-8 -*-
"""
Created on Tue Jan 24 10:27:34 2017
@author: mbialoncz
"""
# -*- coding: utf-8 -*-
from __future__ import division
import numpy as np
import scipy.linalg as lin
import scipy.optimize as opt
import math
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import sys
import random
from mean_field import *
import sys
N = 6
kappa = 1.3
def Energy_condensate_full(Q, F1, x, y, H, mu, kappa, Ns) :
if Q==0 and F1 ==0 :
return 1e14
m = find_minimum(Q, F1, mu, kappa, Ns)
if m[0] < H/2 :
return 1e14
result = 0
for n1 in range(Ns) :
for n2 in range(Ns) :
M, dim = HamiltonianMatrix(n1, n2, Q, F1, 0, H, mu, kappa, Ns, 'T1')
B = np.identity(dim)
B[dim/2:dim, dim/2:dim] = -np.identity(dim/2)
eig = np.absolute(np.real(lin.eigvals(np.dot(B,M))))
result += sum(eig)/2
vec = [x[Ns * n1 + n2], np.conjugate(y[Ns * ((Ns - n1) % Ns) + (Ns - n2) % Ns])]
result += np.dot(vec, np.dot(np.conj(vec).T, M))
return result - 3 * Ns ** 2 * (np.abs(F1)**2 - np.abs(Q)**2)/2 - Ns**2 * mu*(1. + kappa) + Ns * H
def find_minimum(Q, F1, mu, kappa, Ns) :
m = 100000000
k_min = [0,0]
for n1 in range(Ns):
for n2 in range(Ns) :
k1 = 2 * n1 * np.pi/Ns
k2 = 2 * n2 * np.pi/Ns
a = mu + 2 * J * F1 * (np.cos(k1) + np.cos(k2) + np.cos(k1+k2))
b = 2 * J * Q * (np.sin(k1) + np.sin(k2) - np.sin(k1+k2))
Ek2 = a**2 - b**2
if Ek2 < m :
m = Ek2
k_min = [k1,k2]
return [m]+k_min
def Average_number(Q, F1, x, y, H, mu, kappa, Ns) :
result = 0
for n1 in range(Ns) :
for n2 in range(Ns) :
result += np.abs(x[Ns * n1 + n2])**2 + np.abs(y[Ns * n1 + n2])**2
return ParticleNumber(Q, F1, 0, H, mu, kappa, Ns, 'T1') + result/(Ns*Ns)
def Energy_condensate(params, H, kappa, Ns) :
Q = params[0]
F1 = params[1]
# F1 = params[1]
# xc1 = params[2] + params[3] * 1j
# yc1 = params[4] + params[5] * 1j
# xc2 = params[6] + params[7] * 1j
# yc2 = params[8] + params[9] * 1j
x = np.zeros(Ns**2)
y = np.zeros(Ns**2)
# x[Ns**2/3 + Ns/3] = xc1
# y[Ns**2/3 + Ns/3] = yc1
# x[2/3 * Ns**2 + 2/3 * Ns] = xc2
# y[2/3 * Ns**2 + 2/3 * Ns] = yc2
return Energy_condensate_reduced(Q, F1, x, y, H, kappa, Ns)
def Bis_condensate(a, b, Q, F1, x, y, H, kappa, Ns) :
# while (ParticleNumber(Q, F1, F2, H, a, kappa, Ns, ansatz) == np.inf or
# ParticleNumber(Q, F1, F2, H, a, kappa, Ns, ansatz) == np.nan) :
#
# while ParticleNumber(Q, F1, F2, H, b, kappa, Ns, ansatz) < kappa :
# b=(a+b)/2
#
# a = (a+b)/2
#
# if ParticleNumber(Q, F1, F2, H, a, kappa, Ns, ansatz) <= kappa :
# a = 2*a - b
c = 0
it = 0
while (Average_number(Q, F1, x, y, H, b, kappa,Ns) == np.inf or
np.isnan(Average_number(Q, F1, x,y, H, b, kappa,Ns)) or
Average_number(Q, F1,x, y, H, b, kappa,Ns) >= kappa):
b = 2 * b
while (Average_number(Q, F1,x,y, H, a, kappa,Ns) == np.inf or
np.isnan(Average_number(Q, F1,x, y, H, a, kappa,Ns)) or
np.absolute(Average_number(Q, F1, x, y, H, a, kappa,Ns) -
Average_number(Q,F1, x, y, H, b, kappa, Ns)) > 0.00001) :
c = (a+b)/2
it += 1
if it > 30:
return c
#print Q, c
if (np.sign(Average_number1(Q, F1, x, y, H, c, kappa, Ns) - kappa) ==
np.sign(Average_number1(Q, F1, x, y, H, b, kappa, Ns)-kappa)) :
b = c
else :
a = c
return c
def Energy_condensate_reduced(Q, F1, x, y, H, kappa, Ns) :
mu = Bis_condensate(0., 5., Q, F1, x, y, H, kappa, Ns)
return Energy_condensate_full(Q, F1, x, y, H,mu, kappa, Ns)
def Average_number1(Q, F1, x, y, H, mu, kappa, Ns) :
result = 0
for n1 in range(Ns) :
for n2 in range(Ns) :
k1 = 2 * n1 * np.pi/Ns
k2 = 2 * n2 * np.pi/Ns
a = mu + 2 * J * F1 * (np.cos(k1) + np.cos(k2) + np.cos(k1+k2))
b = 2 * J * Q * (np.sin(k1) + np.sin(k2) - np.sin(k1+k2))
# print a/np.sqrt(a**2 - b**2)
result += a/np.sqrt(a**2 -b**2) + np.abs(x[n1 * Ns + n2])**2 + np.abs(y[n1*Ns + n2])**2
return result/Ns**2 - 1
def change_parameters(params, H, kappa, Ns) :
x = np.zeros(Ns**2, dtype = complex)
y = np.zeros(Ns**2, dtype = complex)
for i in range(Ns**2) :
x[i] = params[2*i] + params[2 * i + 1] * (1j)
for i in range(Ns**2, 2 * Ns**2) :
y[i-Ns**2] = params[2*i] + params[2*i + 1] * (1j)
Q = params[4 * Ns**2]
F1 = params[4 * Ns**2 + 1]
return Energy_condensate_reduced(Q, F1, x, y, H, kappa, Ns)
def check_if_condense(H, kappa, Ns) :
f = lambda x : change_parameters(x, H, kappa, Ns)
# f1 = lambda x : Energy_condensate_reduced(x[0], 0 , np.zeros(Ns**2, dtype = complex), np.zeros(Ns**2, dtype = complex), H, kappa, Ns)
# solucja1 = opt.minimize(f1, 5. , method = 'Nelder-Mead')
# energy_without = solucja1.fun
# print 'energy without condensation = ', solucja1.fun, 'parameter = ', solucja1.x
#
m = 1e14
m_params = np.zeros(4 * Ns**2 + 2)
for _ in range(10) :
params = list(np.random.rand(4*Ns**2)) + [10 * np.random.rand()] + [0.]
solucja = opt.minimize(f, params, method = 'Nelder-Mead')
print 'kappa = ', kappa, 'H = ', H, 'run = ', _ , 'energy = ', solucja.fun, 'param = ', solucja.x
if solucja.fun < m :
m = solucja.fun
m_params = solucja.x
print "final solution", m, x
if __name__ == "__main__":
check_if_condense(sys.argv[1], sys.argv[2], 6)
#x0 = np.zeros(N**2, dtype = complex)
#y0 = np.zeros(N**2, dtype = complex)
#x1 = np.zeros(N**2, dtype = complex)
#y1 = np.zeros(N**2, dtype = complex)
#for n1 in range(N) :
# for n2 in range(N) :
# x0[N * n1 + n2] = 0
# y0[N * n1 + n2] = 0
#x0[N**2/3 + N/3] = np.random.rand() + np.random.rand()*1j
#y0[N**2/3 + N/3] = np.random.rand() + np.random.rand()*1j
#Q0 = 0.2
#F10 = 0.
#mu0 = 2.5
#x0[N**2/3 + N/3] = 1.
#y0[N**2/3 + N/3] = 1j
#x0[2/3 * N**2 + 2/3 * N] = 1
#y0[2/3 * N**2 + 2/3 * N] = -1j
#print find_minimum(Q0, 0.49, mu0 ,kappa, N)
#print Average_number(Q0, F10, x1, y1, 0., mu0, kappa, N)
#print Average_number1(Q0, F10, x0, y0, 0., mu0, )
#f1 = lambda params1 : Energy_condensate([params1[0], 0, params1[1],params1[2],params1[3],params1[4],params1[5],params1[6],params1[7],params1[8]],0,kappa,N)
#params0 = [0.2, 1., 0, 0, 0, 0, 0, 0, 1, 0]
#
#for kappa in np.arange(0.2, 1.4, 0.2) :
# m=1000000000
# po = np.zeros(9)
# for _ in range(20) :
#
# params01 = [5.] + list(np.random.rand(8))
# print params01
# solucja = opt.minimize(f1, params01, method = 'Nelder-Mead')
# print 'sol' , _, solucja.x, solucja.fun
# if solucja.fun <= m :
# po = solucja.x
# m = solucja.fun
# print kappa, m, po
#
#print 'result', m
#
#f = lambda params : Energy_condensate(params, 0., kappa, N)
#
#solucja = opt.minimize(f1, params01, method = 'Nelder-Mead')
#print 'sol' , solucja.x
#print Average_number(Q0, F10, x0, y0, 0., a, kappa, N)
#
#mu_values = np.arange(1.2,1.5,0.05)
#print Average_number(Q0, F10,x0,y0,0,1.0311, kappa, N)
#print Bis_condensate(0, 5, Q0, 0, x0, y0, 0, kappa, N)
#
#Q_values = np.arange(-6,6, 0.1)
#F_values = np.arange(-0.5,0.5, 0.1)
#particle_values = [Average_number(Q0, F10, x0, y0, 0., mu, kappa, N) for mu in mu_values]
#particle_values1 = [Average_number1(Q0, F10, x0, y0, 0., mu, kappa, N) for mu in mu_values]
#Energy_values = [np.abs(Energy_condensate_reduced(Q, 0, x0, y0, 0.0, kappa, N)) for Q in Q_values]
##print particle_values
#print Energy_values
#mu_v = [Bis_condensate(0,5,Q,0,x0,y0,0,kappa, N) for Q in Q_values]
#print Bis_condensate(0,5,Q,0,x0,y0,0,kappa, N)
#print 'av', Average_number1(Q, 0.0,x0,y0, 0, Bis_condensate(0,5,Q,0,x0,y0,0,kappa, N), kappa,N)
#Energy_values = [np.abs(f1([Q])) for Q in Q_values]
#plt.plot(Q_values, Energy_values)
#plt.savefig('dupa1.jpg')